from utils import *
from sklearn.model_selection import train_test_split
df = pd.read_excel('data/DS_assessment.xlsx', sheet_name = 'Data')
df.shape
(5000, 13)
Standardize column names to lowercase, with spaces denoted by _
df = standardize_column_names(df, custom_mapping = {'CCAvgSpending': 'cc_avg_spending', 'InternetBanking': 'internet_banking'})
df.columns
Index(['id', 'age', 'experience', 'income', 'postal_code', 'family_size',
'cc_avg_spending', 'education', 'mortgage', 'investment_account',
'deposit_account', 'internet_banking', 'personal_loan'],
dtype='object')
check_missing_columns(df)
| contains_missing | missing_count | missing_percent | |
|---|---|---|---|
| id | False | 0 | 0.00 |
| age | False | 0 | 0.00 |
| experience | False | 0 | 0.00 |
| income | True | 20 | 0.40 |
| postal_code | False | 0 | 0.00 |
| family_size | True | 9 | 0.18 |
| cc_avg_spending | False | 0 | 0.00 |
| education | False | 0 | 0.00 |
| mortgage | False | 0 | 0.00 |
| investment_account | False | 0 | 0.00 |
| deposit_account | False | 0 | 0.00 |
| internet_banking | False | 0 | 0.00 |
| personal_loan | False | 0 | 0.00 |
income and family_size columns contain missing values. Given that the number and percentage of records with missing income (0.4%) or family_size (0.18%) values is very small and insignificant, let's drop these records.
df.dropna(inplace = True)
df.shape
(4971, 13)
df.postal_code = df.postal_code.astype('category')
df.dtypes
id int64 age int64 experience int64 income float64 postal_code category family_size float64 cc_avg_spending float64 education object mortgage int64 investment_account int64 deposit_account int64 internet_banking object personal_loan object dtype: object
mapping = {'NO': 0, 'YES': 1}
df.internet_banking = df.internet_banking.map(mapping)
df.personal_loan = df.personal_loan.map(mapping)
print(df.dtypes)
print(f'\nUnique values in internet_banking: {df.internet_banking.unique()}')
print(f'Unique values in personal_loan: {df.personal_loan.unique()}')
id int64 age int64 experience int64 income float64 postal_code category family_size float64 cc_avg_spending float64 education object mortgage int64 investment_account int64 deposit_account int64 internet_banking int64 personal_loan int64 dtype: object Unique values in internet_banking: [0 1] Unique values in personal_loan: [0 1]
Let's take a look at the summary statistics of the data to detect any potential outliers or errorneous data.
df.describe()
| id | age | experience | income | family_size | cc_avg_spending | mortgage | investment_account | deposit_account | internet_banking | personal_loan | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 | 4971.000000 |
| mean | 2505.909877 | 45.334339 | 20.100583 | 73.805472 | 2.394689 | 1.937556 | 56.626836 | 0.104607 | 0.060350 | 0.596862 | 0.096359 |
| std | 1439.973439 | 11.458282 | 11.462613 | 46.074179 | 1.147091 | 1.746019 | 101.813329 | 0.306077 | 0.238158 | 0.490577 | 0.295112 |
| min | 1.000000 | 23.000000 | -3.000000 | 8.000000 | 1.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 25% | 1261.500000 | 35.000000 | 10.000000 | 39.000000 | 1.000000 | 0.700000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 50% | 2506.000000 | 45.000000 | 20.000000 | 64.000000 | 2.000000 | 1.500000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| 75% | 3750.500000 | 55.000000 | 30.000000 | 98.000000 | 3.000000 | 2.500000 | 101.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| max | 5000.000000 | 67.000000 | 43.000000 | 224.000000 | 4.000000 | 10.000000 | 635.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
It could be observed that the minimum value for experience is -3. This does not make sense, as it is not possible for anyone to have negative years of professional experience. Let's dive deeper to see how many records contain negative experience values.
neg_exp = df[df.experience < 0]
neg_exp.shape
(51, 13)
There are 51 records with negative experience. Percentage wise, these records account for 1.03% (i.e. 51/4971) of the records, which is a very small insignificant proportion. Hence, let's drop these records as well.
df = df[df.experience >= 0]
df.shape
(4920, 13)
Perform Feature Engineering¶
Features to create¶
- income_cc_spending_diff: Difference between annual income and annual credit card spending (i.e. income - 12 x cc_avg_spending)
- cc_spending_income_ratio: Ratio between annual credit card spending and annual income (i.e. 12 x cc_avg_spending / income)
- mortage_income_diff: Difference between home mortgage value and annual income and (i.e. mortage - income)
- mortage_income_ratio: Ratio between home mortgage value and annual income (i.e. mortage / income)
df['income_cc_spending_diff'] = df['income'] - 12 * df['cc_avg_spending']
df['cc_spending_income_ratio'] = 12 * df['cc_avg_spending'] / df['income']
df['mortage_income_diff'] = df['mortgage'] - df['income']
df['mortage_income_ratio'] = df['mortgage'] / df['income']
df.head(1)
| id | age | experience | income | postal_code | family_size | cc_avg_spending | education | mortgage | investment_account | deposit_account | internet_banking | personal_loan | income_cc_spending_diff | cc_spending_income_ratio | mortage_income_diff | mortage_income_ratio | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 25 | 1 | 49.0 | 91107 | 4.0 | 1.6 | Undergrad | 0 | 1 | 0 | 0 | 0 | 29.8 | 0.391837 | -49.0 | 0.0 |
plot_categories_distribution(df, 'personal_loan', width = 800, height = 400)
It could be observed that the dataset is imbalanced in terms of the target variable, personal_loan. The number of customers that do not take up the personal loan (i.e. personal_loan = 0) is more than 9x the number of customers that take up the loan (i.e. personal_loan = 1).
Analyse the probability of personal_loan = 1 given a categorical value¶
Probability of personal_loan = 1 given postal_code
loan_probs = compute_loan_probability(df, category_col = 'postal_code', ascending = False)
loan_probs.head(10)
| postal_code | personal_loan | probability | |
|---|---|---|---|
| 819 | 95135 | 1 | 0.666667 |
| 921 | 96008 | 1 | 0.666667 |
| 501 | 93311 | 1 | 0.500000 |
| 723 | 94705 | 1 | 0.500000 |
| 289 | 92056 | 1 | 0.500000 |
| 175 | 91129 | 1 | 0.500000 |
| 589 | 94108 | 1 | 0.500000 |
| 11 | 90016 | 1 | 0.500000 |
| 53 | 90059 | 1 | 0.500000 |
| 469 | 93022 | 1 | 0.400000 |
The table above suggests that there is some form of correlation between where the customer stays (i.e. postal_code) and whether he will take up the personal loan (i.e. personal_loan). Customers living at certain postal codes are more likely to take up the personal loan.
For example, it could be observed that customers living at 95135 and 96008 postal codes are very likely to take up the personal loan, each having a $\frac{2}{3}$ chance of doing so.
loan_probs.tail(10)
| postal_code | personal_loan | probability | |
|---|---|---|---|
| 431 | 92735 | 1 | 0.0 |
| 403 | 92661 | 1 | 0.0 |
| 425 | 92705 | 1 | 0.0 |
| 423 | 92704 | 1 | 0.0 |
| 421 | 92703 | 1 | 0.0 |
| 417 | 92694 | 1 | 0.0 |
| 415 | 92692 | 1 | 0.0 |
| 413 | 92691 | 1 | 0.0 |
| 407 | 92673 | 1 | 0.0 |
| 933 | 96651 | 1 | 0.0 |
On the contrary, customers living at postal codes such as 92735, 92661, 92705 etc, are unlikely to take up the personal loan, each having a zero probability of doing so based on the provided dataset.
plot_category_loan_distribution(df, category_col = 'education')
The plot above suggests that there is some form of correlation between a customer's education level (i.e. education) and whether he takes up the personal loan (i.e. personal_loan).
For instance, it could be observed that undergrads are less likely to take up the personal loan, only having a 0.045 probability of doing so, as compared to graduates and customers with advanced degrees, which have a 0.132 and 0.138 proability of taking up the personal loan correspondingly.
plot_category_loan_distribution(df, category_col = 'investment_account', height = 400)
The plot above suggests a weak correlation between investment_account and personal_loan given that the probability of personal loan take up for customers who have an investment account with the bank (i.e. 0.117) is slightly higher than those without (i.e. 0.095).
plot_category_loan_distribution(df, category_col = 'deposit_account', height = 400)
The plot above suggests a strong correlation between deposit_account and personal_loan. Customers who have a deposit account with the bank (i.e. 0.47 probability) are ~6x more likely to take up the personal loan as compared to customers without (i.e. 0.073 probability).
plot_category_loan_distribution(df, category_col = 'internet_banking', height = 400)
The plot above suggests an extremely weak correlation between internet_banking and personal_loan. Customers who use internet banking and customers who do not use internet banking are equally likely to take up the personal loan, given that the probability of personal loan take up for both groups is about the same at ~0.1.
Analyse the correlation between numerical feature values and personal_loan¶
px.box(df, x = 'age', color = 'personal_loan')
From the plot above, it could be observed that the age profile for customers who take up the personal loan (i.e. median 45) is similar to that of customers who do not take up the personal loan (i.e. median 46), given the similar median, q1 and q3 for both groups.
Thus it could be surmised that age is unlikely to be an important factor in determining whether a customer will take up the personal loan.
px.box(df, x = 'experience', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan (i.e. median 20) have similar number of years of professional experience to customers who do not (i.e. median 20), given the similar median, q1 and q3 for both groups.
Thus it could be surmised that years of professional experience is unlikely to be an important factor in determining whether a customer will take up the loan.
px.box(df, x = 'income', color = 'personal_loan')
From the plot above, it could be observed that in general, customers who take up the personal loan tend to have higher annual income. The median annual income for customers who take up the personal loan is 143K whereas the median annual income for those who do not is 59K.
px.box(df, x = 'family_size', color = 'personal_loan')
The plot above suggests that customers who take up the personal loan tend to have larger family size. The median family size for customers who take up the personal loan is 3 while the median family size for those who do not is 2.
px.box(df, x = 'cc_avg_spending', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan tend to have higher average monthly credit card spending. The median average monthly credit card spending for customers who take up the personal loan is 3.8K whereas the median average monthly credit card spending for customers who do not is 1.4K.
px.box(df, x = 'mortgage', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan (i.e. median 0) have similar home mortage values as customers who do not (i.e. median 0), given the similar min, median and q1 for both groups.
Thus it could be surmised that a customer's home mortage value is unlikely to be an important factor in deciding whether he will take up the loan.
px.box(df, x = 'income_cc_spending_diff', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan tend to have a larger disparity between their annual income and annual credit card spending. The median disparity for customers who take up the personal loan is 95K whereas the median disparity for customers who do not is 36.8K.
px.box(df, x = 'cc_spending_income_ratio', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan tend to have a slightly higher credit card spending to income ratio (i.e. median 0.352) than customers who do not (i.e. median 0.314).
px.box(df, x = 'mortage_income_diff', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan tend to have a more negative difference between their home mortage value and annual income. The median difference for customers who take up the personal loan is -118K while the median difference for customers who do not is -40K.
px.box(df, x = 'mortage_income_ratio', color = 'personal_loan')
From the plot above, it could be observed that customers who take up the personal loan (i.e. median 0) have a similar home mortage value to annual income ratio to customers who do not (i.e. median 0), given the similar min, median and q1 for both groups.
Thus it could be surmised that a customer's home mortage value to annual income ratio is unlikely to be an important factor in deciding whether he will take up the loan.
Encode categorical features into numerical values¶
df, encoder_dict = encode_categorical_features(df)
Perform stratified train test split based on target variable, personal_loan¶
train, test = train_test_split(df, test_size = 0.3, random_state = 0, stratify = df.personal_loan)
train = train.reset_index(drop = True)
test = test.reset_index(drop = True)
print(f'train shape: {train.shape}')
print(f'test shape: {test.shape}')
train shape: (3444, 17) test shape: (1476, 17)
Perform Nested Stratified K-Fold Cross-Validation¶
We perform nested stratified k-fold cross-validation to estimate:
- The average model performance on the full train dataset for each model
- The final number of boosting rounds required for training with the full train dataset for each model
How this works¶
- We first stratify split our train dataset into N partitions, based on the personal_loan label.
- We keep 1 partition as the held-out test set and use the remaining N - 1 partitions for model training and validation.
- We then further stratify split the N - 1 parititions dataset into another K partitions, based on the personal_loan label and perform K-fold cross validation with it. How this works is that we use K - 1 partitions for training and the remaining 1 partition for hyperparameter tuning. We repeat this process iteratively until all K partitions have been used for hyperparameter tuning. From these series of experiments, we estimate the optimal set of hyperparameters to use for training on the full N - 1 partitions dataset.
- Following which, we train our model with the full N - 1 partitions dataset and the optimal set of hyperparameters.
- After that, we compute the performance of our model (i.e. trained on N - 1 partitions dataset) on the held-out test set.
- We repeat steps 2 - 5 iteratively until all N partitions have been used as the held-out test set.
- Finally, we compute the average test performance of the models based on all N held-out test sets.
Features used for model training¶
Target Variable:
- personal_loan
Numerical Features:
- age
- experience
- income
- family_size
- cc_avg_spending
- mortgage
- income_cc_spending_diff
- cc_spending_income_ratio
- mortage_income_diff
- mortage_income_ratio
Categorical Features:
- postal_code
- education
- investment_account
- deposit_account
- internet_banking
Model Selection¶
For the purpose of model comparison and evaluation, two tree-based models, CatBoost and LightGBM were chosen. The reason why tree-based models were chosen is because they tend to deliver state-of-the-art performance on tabular data problems due to the use of bagging and boosting.
CatBoost and LightGBM were chosen because of their:
- Fast training and inference speed
- Support for categorical features
- Support for regularization
- Superior model performance as compared to their other tree-based counterparts
Model Evaluation Metrics¶
Given the class imbalance, accuracy might not be the most appropriate evaluation metric to use, as it is biased towards the majority class (i.e. personal_loan = 0). Instead, f1 score might be a more appropriate metric, given that it is the harmonic mean of precision and recall, and hence unbiased towards either of the classes.
Precision:
- Measures the loan take up rate
- Precision = $\frac{\text{No of customers correctly predicted by the model to take up the loan}}{\text{Total no of customers predicted by the model to take up the loan}}$
- From a business standpoint, we would like to maximize precision as higher precision means that we are targeting the correct customers (i.e. those that will take up the personal loan) and lowering the costs and efforts spent on the wrong customers (i.e. those that will not take up the personal loan). Thus, the better model is the one with higher precision.
Recall
- Recall = $\frac{\text{No of customers correctly predicted by the model to take up the loan}}{\text{Actual total no of customers that take up the loan}}$
- From a business perspective, we would like to maximize recall as higher recall means that we are targeting a larger proportion of the customers that will take up the loan; i.e. casting a wider net to include more of the customers that will take up the loan. Hence, the better model is the one with higher recall as well.
There is however a trade-off between precision and recall. Improving one usually will come at the expense of the other. For this exercise, we assume that both precision and recall are equally important to the business. In such a case, f1 score is the appropriate metric to use, as it provides a balance between precision and recall.
num_folds = 5
# Factor to scale num_boost_rounds by in model training
# Factor is calculated based on the ratio of full dataset size / dataset size used for training during each fold of cross validation
scaling_factor = num_folds / (num_folds - 1)
threshold = 0.5
label_col = 'personal_loan'
num_features = ['age', 'experience', 'income', 'family_size', 'cc_avg_spending',
'mortgage', 'income_cc_spending_diff', 'cc_spending_income_ratio',
'mortage_income_diff', 'mortage_income_ratio']
cat_features = ['postal_code', 'education', 'investment_account', 'deposit_account', 'internet_banking']
features = num_features + cat_features
Perform Nested Stratified K-Fold Cross-Validation for LightGBM¶
model_name = 'lightgbm'
stratified_kfold_results = nested_stratified_kfold_cv(train, features, cat_features, model_name, num_folds = num_folds, scaling_factor = scaling_factor)
Outer train shape: (2755, 17) test shape: (689, 17) Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.323247 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1838 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [33] valid_0's binary_logloss: 0.0718844 Best iteration: 33 Validation f1 score: 0.8653846153846154 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000326 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1854 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [38] valid_0's binary_logloss: 0.0397198 Best iteration: 38 Validation f1 score: 0.8952380952380953 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000168 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1829 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [41] valid_0's binary_logloss: 0.0393219 Best iteration: 41 Validation f1 score: 0.9357798165137615 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000170 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1840 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [31] valid_0's binary_logloss: 0.0501947 Best iteration: 31 Validation f1 score: 0.897196261682243 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.001800 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1847 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [51] valid_0's binary_logloss: 0.0394272 Best iteration: 51 Validation f1 score: 0.9259259259259259 Average best iteration: 38.8 Scaled average best iteration: 48 [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 268, number of negative: 2487 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000158 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1945 [LightGBM] [Info] Number of data points in the train set: 2755, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097278 -> initscore=-2.227845 [LightGBM] [Info] Start training from score -2.227845 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Test f1 score: 0.9333333333333335 Outer train shape: (2755, 17) test shape: (689, 17) Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000162 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1830 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [37] valid_0's binary_logloss: 0.0322061 Best iteration: 37 Validation f1 score: 0.9333333333333333 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000141 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1818 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [39] valid_0's binary_logloss: 0.0278291 Best iteration: 39 Validation f1 score: 0.923076923076923 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000302 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1828 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [39] valid_0's binary_logloss: 0.0685846 Best iteration: 39 Validation f1 score: 0.8888888888888888 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000147 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1829 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [40] valid_0's binary_logloss: 0.0392562 Best iteration: 40 Validation f1 score: 0.9038461538461539 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000387 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1837 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [34] valid_0's binary_logloss: 0.0391605 Best iteration: 34 Validation f1 score: 0.9142857142857143 Average best iteration: 37.8 Scaled average best iteration: 47 [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 268, number of negative: 2487 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000184 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1929 [LightGBM] [Info] Number of data points in the train set: 2755, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097278 -> initscore=-2.227845 [LightGBM] [Info] Start training from score -2.227845 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Test f1 score: 0.887218045112782 Outer train shape: (2755, 17) test shape: (689, 17) Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000302 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1833 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [33] valid_0's binary_logloss: 0.0410381 Best iteration: 33 Validation f1 score: 0.9320388349514563 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000168 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1844 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [38] valid_0's binary_logloss: 0.0355839 Best iteration: 38 Validation f1 score: 0.9259259259259259 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000316 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1842 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [36] valid_0's binary_logloss: 0.0434878 Best iteration: 36 Validation f1 score: 0.9056603773584906 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000318 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1757 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [42] valid_0's binary_logloss: 0.0467974 Best iteration: 42 Validation f1 score: 0.9215686274509804 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000155 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1828 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [36] valid_0's binary_logloss: 0.0446655 Best iteration: 36 Validation f1 score: 0.912621359223301 Average best iteration: 37.0 Scaled average best iteration: 46 [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 268, number of negative: 2487 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000166 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1936 [LightGBM] [Info] Number of data points in the train set: 2755, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097278 -> initscore=-2.227845 [LightGBM] [Info] Start training from score -2.227845 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Test f1 score: 0.8939393939393939 Outer train shape: (2755, 17) test shape: (689, 17) Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000321 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1840 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [39] valid_0's binary_logloss: 0.044607 Best iteration: 39 Validation f1 score: 0.923076923076923 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1989 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000322 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1849 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097550 -> initscore=-2.224749 [LightGBM] [Info] Start training from score -2.224749 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [54] valid_0's binary_logloss: 0.0292189 Best iteration: 54 Validation f1 score: 0.9807692307692307 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000306 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1850 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [45] valid_0's binary_logloss: 0.0408655 Best iteration: 45 Validation f1 score: 0.9215686274509804 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000275 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1858 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [36] valid_0's binary_logloss: 0.0329233 Best iteration: 36 Validation f1 score: 0.9245283018867925 Inner train shape: (2204, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000294 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1838 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [41] valid_0's binary_logloss: 0.0555179 Best iteration: 41 Validation f1 score: 0.9009009009009009 Average best iteration: 43.0 Scaled average best iteration: 53 [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 268, number of negative: 2487 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000681 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1945 [LightGBM] [Info] Number of data points in the train set: 2755, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097278 -> initscore=-2.227845 [LightGBM] [Info] Start training from score -2.227845 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Test f1 score: 0.8854961832061069 Outer train shape: (2756, 17) test shape: (688, 17) Inner train shape: (2204, 17) val shape: (552, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000300 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1834 [LightGBM] [Info] Number of data points in the train set: 2204, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097096 -> initscore=-2.229914 [LightGBM] [Info] Start training from score -2.229914 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [42] valid_0's binary_logloss: 0.0426305 Best iteration: 42 Validation f1 score: 0.9245283018867925 Inner train shape: (2205, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000312 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1834 [LightGBM] [Info] Number of data points in the train set: 2205, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097506 -> initscore=-2.225252 [LightGBM] [Info] Start training from score -2.225252 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [37] valid_0's binary_logloss: 0.0327407 Best iteration: 37 Validation f1 score: 0.9215686274509803 Inner train shape: (2205, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 215, number of negative: 1990 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000378 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1835 [LightGBM] [Info] Number of data points in the train set: 2205, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097506 -> initscore=-2.225252 [LightGBM] [Info] Start training from score -2.225252 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [37] valid_0's binary_logloss: 0.0506723 Best iteration: 37 Validation f1 score: 0.897196261682243 Inner train shape: (2205, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1991 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000145 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1822 [LightGBM] [Info] Number of data points in the train set: 2205, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097052 -> initscore=-2.230416 [LightGBM] [Info] Start training from score -2.230416 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [28] valid_0's binary_logloss: 0.0563715 Best iteration: 28 Validation f1 score: 0.8867924528301887 Inner train shape: (2205, 17) val shape: (551, 17) [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 214, number of negative: 1991 [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000307 seconds. You can set `force_col_wise=true` to remove the overhead. [LightGBM] [Info] Total Bins 1836 [LightGBM] [Info] Number of data points in the train set: 2205, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097052 -> initscore=-2.230416 [LightGBM] [Info] Start training from score -2.230416 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Training until validation scores don't improve for 5 rounds [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Early stopping, best iteration is: [36] valid_0's binary_logloss: 0.04185 Best iteration: 36 Validation f1 score: 0.9357798165137615 Average best iteration: 36.0 Scaled average best iteration: 45 [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 268, number of negative: 2488 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000231 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1931 [LightGBM] [Info] Number of data points in the train set: 2756, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097242 -> initscore=-2.228247 [LightGBM] [Info] Start training from score -2.228247 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf Test f1 score: 0.9172932330827067
Compute average LightGBM performance on validation and test sets
avg_val_f1 = np.mean(stratified_kfold_results['val_f1'])
avg_test_f1 = np.mean(stratified_kfold_results['test_f1'])
avg_num_boost_rounds = int(np.mean(stratified_kfold_results['test_num_boost_rounds']))
print(f'Average validation f1: {avg_val_f1}')
print(f'Average test f1: {avg_test_f1}')
print(f'Average test num_boost_rounds: {avg_num_boost_rounds}')
Average validation f1: 0.9158992119013841 Average test f1: 0.9034560377348646 Average test num_boost_rounds: 47
Train LightGBM on full train dataset
model_path = './models/lgb_model_final.txt'
full_num_boost_rounds = int(np.mean(stratified_kfold_results['test_num_boost_rounds']) * scaling_factor)
print(f' Number of iterations used to train LightGBM model on full dataset: {full_num_boost_rounds}')
lgb_model = train_lgb_model(
train = train,
num_boost_rounds = full_num_boost_rounds,
features = features,
cat_features = cat_features,
model_path = model_path,
)
Number of iterations used to train LightGBM model on full dataset: 59 [LightGBM] [Warning] Categorical features with more bins than the configured maximum bin number found. [LightGBM] [Warning] For categorical features, max_bin and max_bin_by_feature may be ignored with a large number of categories. [LightGBM] [Info] Number of positive: 335, number of negative: 3109 [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000235 seconds. You can set `force_row_wise=true` to remove the overhead. And if memory is not enough, you can set `force_col_wise=true`. [LightGBM] [Info] Total Bins 1991 [LightGBM] [Info] Number of data points in the train set: 3444, number of used features: 15 [LightGBM] [Info] [binary:BoostFromScore]: pavg=0.097271 -> initscore=-2.227926 [LightGBM] [Info] Start training from score -2.227926 [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf [LightGBM] [Warning] No further splits with positive gain, best gain: -inf
Compute LightGBM performance on actual held out test dataset
test_preds = (lgb_model.predict(test[features]) > threshold).astype(int)
lgb_performance_dict = classification_report(test[label_col], test_preds, output_dict = True)['1']
lgb_performance_dict['model'] = model_name
print(classification_report(test[label_col], test_preds))
precision recall f1-score support
0 0.98 0.99 0.99 1332
1 0.94 0.83 0.88 144
accuracy 0.98 1476
macro avg 0.96 0.91 0.93 1476
weighted avg 0.98 0.98 0.98 1476
Perform Nested Stratified K-Fold Cross-Validation for CatBoost¶
model_name = 'catboost'
stratified_kfold_results = nested_stratified_kfold_cv(train, features, cat_features, model_name, num_folds = num_folds, scaling_factor = scaling_factor)
Outer train shape: (2755, 17) test shape: (689, 17) Inner train shape: (2204, 17) val shape: (551, 17) Learning rate set to 0.104877 0: learn: 0.6137099 test: 0.6148079 best: 0.6148079 (0) total: 93.1ms remaining: 9.21s 1: learn: 0.5491618 test: 0.5512964 best: 0.5512964 (1) total: 95.5ms remaining: 4.68s 2: learn: 0.4927994 test: 0.4953503 best: 0.4953503 (2) total: 97.3ms remaining: 3.15s 3: learn: 0.4447187 test: 0.4467030 best: 0.4467030 (3) total: 98.5ms remaining: 2.36s 4: learn: 0.4070794 test: 0.4087971 best: 0.4087971 (4) total: 100ms remaining: 1.91s 5: learn: 0.3737032 test: 0.3759344 best: 0.3759344 (5) total: 104ms remaining: 1.62s 6: learn: 0.3407056 test: 0.3448025 best: 0.3448025 (6) total: 106ms remaining: 1.41s 7: learn: 0.3120391 test: 0.3189019 best: 0.3189019 (7) total: 108ms remaining: 1.24s 8: learn: 0.2884489 test: 0.2959632 best: 0.2959632 (8) total: 109ms remaining: 1.1s 9: learn: 0.2677752 test: 0.2749242 best: 0.2749242 (9) total: 111ms remaining: 996ms 10: 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bestTest = 0.04656710926 bestIteration = 98 Shrink model to first 99 iterations. Best iteration: 98 Validation f1 score: 0.9199999999999999 Inner train shape: (2204, 17) val shape: (551, 17) Learning rate set to 0.104877 0: learn: 0.6109688 test: 0.6089537 best: 0.6089537 (0) total: 1.25ms remaining: 124ms 1: learn: 0.5476995 test: 0.5431491 best: 0.5431491 (1) total: 3.42ms remaining: 168ms 2: learn: 0.4918544 test: 0.4870208 best: 0.4870208 (2) total: 5.21ms remaining: 169ms 3: learn: 0.4455739 test: 0.4391190 best: 0.4391190 (3) total: 6.81ms remaining: 163ms 4: learn: 0.4049850 test: 0.3978825 best: 0.3978825 (4) total: 8.38ms remaining: 159ms 5: learn: 0.3670385 test: 0.3600460 best: 0.3600460 (5) total: 9.97ms remaining: 156ms 6: learn: 0.3334514 test: 0.3270983 best: 0.3270983 (6) total: 11.5ms remaining: 153ms 7: learn: 0.3087096 test: 0.3022051 best: 0.3022051 (7) total: 13.2ms remaining: 152ms 8: learn: 0.2828793 test: 0.2761500 best: 0.2761500 (8) total: 14.6ms remaining: 148ms 9: learn: 0.2605898 test: 0.2526662 best: 0.2526662 (9) total: 15.9ms 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Compute average CatBoost performance on validation and test sets
avg_val_f1 = np.mean(stratified_kfold_results['val_f1'])
avg_test_f1 = np.mean(stratified_kfold_results['test_f1'])
avg_num_boost_rounds = int(np.mean(stratified_kfold_results['test_num_boost_rounds']))
print(f'Average validation f1: {avg_val_f1}')
print(f'Average test f1: {avg_test_f1}')
print(f'Average test num_boost_rounds: {avg_num_boost_rounds}')
Average validation f1: 0.9225705696238471 Average test f1: 0.9281793928719436 Average test num_boost_rounds: 123
Train CatBoost on full train dataset
model_path = './models/cb_model_final.cbm'
full_num_boost_rounds = int(np.mean(stratified_kfold_results['test_num_boost_rounds']) * scaling_factor)
print(f' Number of iterations used to train CatBoost model on full dataset: {full_num_boost_rounds}')
cb_model = train_catboost_model(
train = train,
num_boost_rounds = full_num_boost_rounds,
features = features,
cat_features = cat_features,
model_path = model_path,
)
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Compute CatBoost performance on actual held out test dataset
test_preds = (cb_model.predict(test[features]) > threshold).astype(int)
cb_performance_dict = classification_report(test[label_col], test_preds, output_dict = True)['1']
cb_performance_dict['model'] = model_name
print(classification_report(test[label_col], test_preds))
precision recall f1-score support
0 0.98 1.00 0.99 1332
1 0.98 0.85 0.91 144
accuracy 0.98 1476
macro avg 0.98 0.92 0.95 1476
weighted avg 0.98 0.98 0.98 1476
Model Evaluation¶
performance = {
'model': [],
'precision': [],
'recall': [],
'f1-score': [],
}
for k, v in performance.items():
v.append(lgb_performance_dict[k])
v.append(cb_performance_dict[k])
pd.DataFrame(performance)
| model | precision | recall | f1-score | |
|---|---|---|---|---|
| 0 | lightgbm | 0.937008 | 0.826389 | 0.878229 |
| 1 | catboost | 0.976000 | 0.847222 | 0.907063 |
From the table above, it could be observed that CatBoost outperforms LightGBM in all 3 metrics, precision, recall and f1-score. Hence, CatBoost is the recommended model to use for this problem.
Explain how different features impact model predictions with SHAP values¶
import shap
explainer = shap.TreeExplainer(cb_model)
shap_values = explainer(test[features])
IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
Overall Feature Importance¶
max_display = 15
shap.plots.bar(shap_values, max_display = max_display)
From the plot above, it could be observed that the top 5 most influential features, in descending order are:
- income
- cc_avg_spending
- education
- family_size
- income_cc_spending_diff
The bottom feature, postal_code is observed to have minimal to no effect on the model predictions.
Effect of feature values on model predictions¶
shap.summary_plot(shap_values)
No data for colormapping provided via 'c'. Parameters 'vmin', 'vmax' will be ignored
# Inverse transform education
encoder_dict['education'].inverse_transform([0, 1, 2])
array(['Advanced Degree', 'Graduate', 'Undergrad'], dtype=object)
From the plot above, it could be observed that in general, higher annual income, higher average monthly credit card spending, larger family size, greater difference between annual income and annual credit card spending and having a deposit account, have a positive impact on the model prediction output (i.e. increased probability of personal loan take up).
Conversely, having a lower annual income, lower average monthly credit card spending, smaller family size, smaller difference between annual income and annual credit card spending, not having a deposit account and being an 'Undergrad' have a negative impact on the model prediction output (i.e. decreased probability of personal loan take up).
Local contribution of feature values on model prediction for a single observation¶
Local contribution of features values on model prediction, personal_loan = 1 for a single observation
idx = test[test.personal_loan == 1].index[0]
print(test.iloc[idx])
shap.plots.waterfall(shap_values[idx], max_display = max_display)
id 994.000000 age 41.000000 experience 15.000000 income 185.000000 postal_code 125.000000 family_size 1.000000 cc_avg_spending 3.600000 education 1.000000 mortgage 0.000000 investment_account 0.000000 deposit_account 0.000000 internet_banking 0.000000 personal_loan 1.000000 income_cc_spending_diff 141.800000 cc_spending_income_ratio 0.233514 mortage_income_diff -185.000000 mortage_income_ratio 0.000000 Name: 13, dtype: float64
From the plot above, it could be observed that having a high annual income (i.e. 185K), high average monthly credit card spending (i.e. 3.6K) and being a 'Graduate' heavily influences the model to predict that the customer will take up the personal loan.
Local contribution of features values on model prediction, personal_loan = 0 for a single observation
idx = test[test.personal_loan == 0].index[-1]
print(test.iloc[idx])
shap.plots.waterfall(shap_values[idx], max_display = max_display)
id 823.00 age 61.00 experience 35.00 income 60.00 postal_code 462.00 family_size 3.00 cc_avg_spending 1.40 education 0.00 mortgage 0.00 investment_account 0.00 deposit_account 0.00 internet_banking 0.00 personal_loan 0.00 income_cc_spending_diff 43.20 cc_spending_income_ratio 0.28 mortage_income_diff -60.00 mortage_income_ratio 0.00 Name: 1475, dtype: float64
From the plot above, it could be observed that having a low annual income (i.e. 60K) and low average monthly credit card spending (i.e. 1.4K) influences the model to predict that the customer is very unlikely to take up the personal loan. Conversely, having an 'Advanced Degree', influences the model to predict that the customer is more likely to take up the personal loan.